Bounded game-theoretic semantics for modal mu-calculus

Lauri Hella, Antti Kuusisto, Raine Rönnholm

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We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models. We also use the GTS to identify new alternative variants of the mu-calculus, including close variants of the logic with PTime model checking; variants with iteration limited to finite ordinals; and other systems where the semantic or syntactic specification of the mu-calculus has been modified in a natural way suggested by the GTS.

Original languageEnglish
Article number104882
Number of pages19
JournalInformation and Computation
Issue numberB
Early online date2022
Publication statusPublished - 2022
Publication typeA1 Journal article-refereed


  • Alternative semantics
  • Bounded semantics
  • Closure ordinals
  • Fixed point approximants
  • Game-theoretic semantics
  • Model-checking
  • Mu-calculus

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


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